The effects on handling qualities of low frequency symmetric elastic mode interaction with the rigid body dynamics of a large flexible aircraft was analyzed by use of a mathematical pilot modeling computer simulation. An extension of the optimal control model for a human pilot was made so that the mode interaction effects on the pilot's control task could be assessed. Pilot ratings were determined for a longitudinal tracking task with parametric variations in the undamped natural frequencies of the two lowest frequency symmetric elastic modes made to induce varying amounts of mode interaction. Relating numerical performance index values associated with the frequency variations used in several dynamic cases, to a numerical Cooper-Harper pilot rating has proved successful in discriminating when the mathematical pilot can or cannot separate rigid from elastic response in the tracking task

Swaim, R. L.

English

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HANDLING QUALITIES OF LARGE FLEXIBLE
CONTROL-CONFIGURED AIRCRAFT
Grant No. NSG 4018
Final Technical Report
for Period
January 1, 1979 - June 30, 1980
(NAS.A-CR-163206) HA NDLIN G QUALITIES OF 	 NSO- 25344
LARGE FLEXIBLE CONTROL-CONFIGURED AIRCRAFT
Final Technical Report, 1 Jan. 1979 - 30
Jun. 1980." , (Oklahoma State Un1v.,
	
Unclas
Stillwater.) 13 p HC A02/MF A01
	
CSCL 01c G3/00 21475
Principal Investigator: Dr. Robert L. Swaim
Division of Engineering, Technology
and Architecture
Oklahoma State University
111 Engineering North
Stillwater, OK 74078
NASA Technical Officer: Mr. Glenn B. Gilyard
Vehicle Dynamics and Control
17^16^b,^^ DivisionNASA Hugh L. Dryden Flight^^
y	 +	 fir, Research Center
JUN 1980
	
^w P.O..	 Box 273
Edwards, CA 93523
RECEIVED	 N
NASA STI FACILM_
ACCESS DEPT.
I
I
Introduction
This Is a final report on Grant No. NSG 4010. The project began on
January 1, 1979 and was to have terminated on December 31, 1979. A no-
cost time extension was requested and approved extend Og the termination
date to June 30, 1950.
Dr. Robert L. Swaim, Principal Investigator, has devoted ten percent
tine throughout the project. OnePh.D. student, Mr, Supat Poopaka, has
been employed fifty percent time throughout the project. Mr. Poopaka is
completing his Ph.D. thesis on the project and expects to complete it and
take the final examination, where he defends the thesis, in September 1900.
Three copies of the thesis will be submitted to the Technical Officer, Mr.
Glenn Gilyard, and two copies to the NASA Scientific and Technical Infor-
mation Facility in late September.
As the details of the research will be documented in the thesis,
this final report on the project will be just a brief summiary.
Problem Statement
The effects on handling qualities of low frequency symuetric elastic
mode interaction with the rigid body dynamics of a large flexible air-
craft was analyzed by use of a mathematical pilot modeling computer
simulation. An extension of the optimal control model for a human pilot
was made so that the mode interaction effects on the pilot's control task
could be assessed. Pilot ratings were determined for a longitudinal
tracking task with parametric variations in the undamped natural frequencies
of the two lowest frequency symmetric elastk. , modes made to induce varying
amounts of mode interaction.
A sununary of our mathematical formulation of the problem is contained
in Attachment 1, which is a paper presented by Mr. Poopaka at the Eleventh
G
-2-
Southwestern Graduate Research Conference in Applied Mechanics held April
11-12, 1980 at Oklahoma State University.
Results
Our approach of relating numerical performance index values associated
with the frequency variations used in several dynamic cases to a numerical
Cooper-Harper pilot rating has proved successful in discriminating when
the mathematical pilot can or cannot separate rigid from elastic response
in the tracking task. The detailed presentation of these results will be
contained in the forthcoming Ph.D. thesis by Mr. Poopaka. An outline of
the thesis content is presented below.
Thesis Outline
I. Introduction
A. Handling Qualities and Pilot Ratings
B. Pilot Rating Assessment Techniques
C. Background on the Effects of Dynamic Aeroelasticity
on Handling Qualities
D. Objectives and $cope of Study
E. Plan of Presentation
II. Literature Survey
A. Past Results on Elastic Airplane Research
III. Equations of Motion
A. Longitudinal Equations of Motion for a FleXible Airplane
B. Turbulence Model
C. Attitude Director Equations
D. B-1 Flight Condition
IV. Pilot Modeling
A. Manual Control and Pilot Models
B. Optimal Control Model
C. Internal Model
D. Closed-Loop Performance Equations
E. Hess's Pilot Rating Method
5
it	 -3-
Thesis Outline (cont.1
V. Effects of Elastic Mode Interaction on Handling Qualities
A. Define Controllable Boundary
B. Controllable Boundary Based on Open-Loop Parameters
VI. Conclusions and Recommendations
VII. Selected Bibliography
VIII. Appendix A. Numerical Values of Stability Derivatives
and Equations of Motion
IX. Appendix B. Derivations Related to Singular Perturbation
Theory
X. Appendix C. Computational Algorithms
Project Reports and Presentations
A list of the reports and presentations generated on the project
is given below.
1. R. L. Swaim and Wen-Yo Yen, "Effects of Dynamic Aeroelasticity on
Aircraft Handling Qualities," Journal of Aircraft, Vol. 16, No. 9,
Sept. 1979, pp. 635-637. Also presented at AIAA Oklahoma Section
Mini-Symposium, University of Oklahoma, Feb. 24, 1979.
2. R. L. Swaim, "Handling Qualities of Large Flexible Aircraft,"
presented at AIAA Oklahoma Section Mini-Symposium, Oklahoma State
Univer5ity, Feb. 23, 1980.
3. Supat Poopaka, "Handling Qualities of Large Flexible Aircraft,"
Ph.D. Thesis Research Proposal, Oklahoma State University, Nov. 21,
1979.
4. Supat Poopaka, "Handling Qualities of Large Flexible Aircraft,"
presented at Eleventh Southwestern Graduate Research Conference in
Applied Mechanics, Oklahoma State University, April 11-12, '1980.
5. R. L. Swaim, "Handling Qualities of Large Flexible Control-Configured
Aircraft," Semi-Annual Status Report on Grant No. NSG 4018, June 22,
1979.
6. R. L. Swaim, "Handling Qualities of Large Flexible Control-Configured
Aircraft," Semi-Annual Status Report on Grant No. NSG 4018, Dec. 31,
1979.
rz
-4-
7. R. L. Swaim, "Handling Qualities of Large Flexible Control-Configured
Aircraft," Final Technical Report on Grant No. NSG 4018 0 June 30, 1980.
8. Supat Poopaka, "Handling Qualities of Large Flexible Aircraft," Ph.D.
Thesis, Oklahoma State University, School of Mechanical and Aerospace
Engineering, to appear Sept. 1980.
9. Supat Poopaka and R. L. Swaim, "A Mathematical Pilot Model for Appli-
cation to Highly Elastic Aircraft Handling Qualities Studies," under
preparation for submission to the Journal of Guidance and Control in
Sept. 1980.
i
i
3
1
HANDLING QUAL I T1 CS OF LAR GE FLEX IBLE AIRCRAFT
Sopat Poopak
School of Mechanical aiid Aerospace Engineering
Oklahoma State University
Aprt l / W
Sunana rX
The effects on handling qualities of elastic mode interaction with
the rigid-body dynamics of a large flexible aircraft are discussed. An
extension of the optimal control model for the human operator is made
so that the mode interaction effects on-the pilot's control task can be
assessed.
Introduction
The handling qualities &re the flying qualities of a piloted air-
craft. They are the characteristics of an aircraft that govern the
ease and precision with which a pilot is able to perform the control task
required in support of the aircraft mission flight phase. The pilot's
subjective opinion on the handling qualities is called a pilot rating
and usually based on the Cooper-Hiper pilot rating scale C1].
The effects of elastic mode interaction on the handling qualities
have been reported recently in Reference 2 based on a ground-based pilot-
flown simulation. In this report we develop an extension of the optimal
control model for the human operator so that the mode interaction effects
on handling qualities can be easily assessed.
Problem Statement
The dynamics of an aircraft to be controlled by the human pilot are
described by a set of small perturbation equations of motion:
xa,,^t) +^ Aa acaW + E & WI) f CtW o)
ya
	
Go, ?Cot ffl + D u.Ct)	 1
F.
•2-
where x x col. (x ,x ,x j, y	 is a turbulence state vector, x
a	 ag ar ae	 ^^)	 ar
is a rigid body states, xae is an elastic body states, u is a control
input, y  is a displayed output, and w is a zero-mean, gaussian, white
noise process with autocovariance.
E j 
`YUd ;Stt,)I - w a(+,-t Z )	 (2)
For a cruise,, level fo ighft condition, eqn. (1) represents the
longitudinal equations of motion and yaIt) is an attitude director equa,,
tion.
n i
Via(#) = 60)-- ^ 1 m  (XP ) , . 0)	 dCl) .. ee ^^^	 (3)j.
where xp indicates pilot fuselage station, ^ (x p ) the slop% of the ath
symmetric elastic mode at that station, F j (t) the generalized displace-
merit; ©(t) the rigid body pitch angle, and 0 M the elastic contribution
to total pil;ch angle (see Fig. 1).
right 1--- tangent ai cmkpi
U
Titch
o 	
orreon
 
Angle at Cockpit
The task of the pilot is to keep the rigid pitch response following
the command director, Since only the total pitch response is shown to
the pilot, therefore he has to distinguish rigid body motion from the
total motion. We want to establish the boundary between when the pilot
can visually separate the rigid body piotion from^he total motion in terms
I	 of undamped natural freyuencie of the elastic modes. The rigid body
r
^3^
E
mock►
 parameters will be ma i n to i nod at the values known to give good
.	 •	 ,	 d,
haiidlinil qualities by" the mole-plar.ement technique while the elastic
mode frequencies will be parametrically varied to introduce the mode in-
teraction. The pilot model developed for computer simulation of this
task is presented in the next section,
The Pilot Model
The optimal control model for the human operator developed here is
a modified version of the standard optimal control model(3,4]. The model
structure is illustrated in Fig. 2.
Ot )
—.^pAirtra(+	 'Xow	 pis lq	 yA^^^yr►AMhlc^	 u4tl`^^P .^
r ODERATOR MODEL + '+HUMAN	 i
I	 Delay ►"lk) N¢ r^
Y
 molar s_ Go^►
+trol() Es/i Ma ii orl ^)
ros
try	 t
f	 ^
Fig, 2 Optimal Control Model for Human Operator
The relation v(t) = r(t-T) is approximated by a first-order Padd'
approximation which can be expressed in the state variable form as
u ct)	 z (a) r(f)
(f7	 ^ I aCt) + ^4 	 (4)
The perceived information y p (t) is a noisy version of ya (t), i.e.,
	
yF^1) = yq M) + 1^y cf)	 (5)
-4-
where vy(t) is a zero-mean, gatevJ gin, white noise with autocovariance
V, dlt,	 (8) i
and Vy is known to scale with mean square of yas
'Vyti I= eye E 1 
yQ'i W1
11	
(7)
where the observation noise/signal ratio ey. = 0.0171.
The pilot generates a command control input m(t) which is then
transformed to r(t) via the relation
T„ rC^) + rCt) - mCi) + v',"66)	 (8)
where Tn is the neuromotor lag matrix and vm(t) is a zero-mean, gaussian,
white noise, with autocovariance
E f a,Ct ') et'/at)I - -j”, J Cis ..tZ) 	 (9)
and V  is known to scale with E(mi(t) 2 ), i.e.,
s
V^,, L e„,, E ►►►^ct^	 (10),
	
a
where the motor noise/signal ratio eni^ = 0.003n.
Equations (4) and (8) may be augmented to (1) to define an aug-
mented system of equations
ac.( t ) = Ae ?CU 4 f3,, mCi) + E c WL(0
(11)
yulf) n C C xC,C{J
—S-
I
when ► 	 A„'	 A« Qq -8„	 o
r .
	 O	 Q TR i	 T.
Cc = [Ca p DA ^^ DA ^ . E: r- x MO` 
O TN
The aircraft dynamics of eqn, (1) can be written in the form
ii(f) _N Art xiti) `f Alz ?C LH) + 13 1 U(f) 4E 1 WW
,M. ,W - A 21 ?c1 (1) t Azz, ?c &M + 8z u cI) + Ez+' O
	
b(4) _ C1 x110 4 Cz Wz.(07 + D Lt(f)	 (l2)
where x 1 is a vector of the rigid body state varia0 es, x 2 is a vector
of the elastic mode state variables, and U is a small positive scalar
constant which can be unknown in this study.
In performing estimation and control command generation, it is nec-
essary for the pilot to have 5 knowledge of the aircraft dynamics, the
human limitation parameters (T,T n ,Vy,Vm) and weighting coefficients of the
performance index. This knowledge is called the internal model. In our
aircraft dynamics model, the display consists of a slowly varying part
due mainly to the rigid body dynamics and a high frequency oscillation
part from the elastic mode. From the past experiment [2) it is evident
that the pilot ignores the low amplitude high freugency oscillation part
of the display. Therefore, in the pilot model, we will I the slowly
varying dynamics subsystem as the internal model.
By the singular perturbation technique [5,6], we can d9compose the
4.
slowly varying part from the system (12) by letting u-o , from which we
get
y^ (f)	 CQ, ?Ct(f ) 4 Dd, WO	 (13)
_.,.. r
k
N
	 w6-
8 Alz Az& 13L
"I
DX p .. Cs, AM 6
where	 AoL ,w Ass — A ll AftL Ate
-1
cA	 c , - G1, Air Ail
Ea, : E, — Ass Aii Es
The pilot control task is assumed to be adequately reflected in the
choice of a control r( • ) that minimizes the performance index
J t 10) " r-#
	
T Igo C YOLI") ay 9d(^) + r' Ct1 4r he"'] dt	 ( 1 4)  7
conditioned on the perceived information y p(-). The command control m(t)
of eqn. (8) is then given by
rA	 .-Lori xslf)	 ^-l i xt(f)	 (15)
i	 r	 --t	 1where	 xs [nd,	
, xt s Cx ,`^, r;j	 Tn Pit P,a.
L! ' [ Lo► 1 i 0]
	
., Lop}, - Pu. Q r ,, P - ^
'i p J s^ hh^ies . ^
fl,s elua4terf
Ao P +?A o + Gp 0b C O .. " C' M ir go P= O 	(16)
A e^ 8 &— Bac	 o	 , _ D
A O = o -&,,r 4/T t 80	 0	 o LC a D^,	 a
O o
	 o	 =
The weighting Q r is chosen such that the resulting T n is equal to 0.1
second, which is a typical value for the human neuromotor lag.
The state x t (t) is the best estimate of x t (t) generated by a Kalman
filter,
?Ct f+) At XtM)+^ B, W(+)4- zC" v^ ' [Lj pH)-Cc,X j0,	 (17)
S.
Y	 r7-
where 1: satisfies the equation
o z Aj	 Es	 co V j^ COX
G D	 TWO
	 TN	 0N.,
	 (18)
Wow
 1
rr wI Q
0'.
Combining egns. (5) with (11), (15) and (17) yields the closed loop
system
Ice w Ac IXc W -- Qc L, Wd + Ec, We f l
	
(Ak- t36 	 (i) +Y_ co vy^[ ,x^ .. Cp X6.^w^C^^^ (1^)
The covariances E(ya (t) 2 ) and E(m i (t) 2 ) for egns. (7) and (10) can be
obtained by solving egns. (19) for cov.(x.c'xt)'
Conclusion
The technique developed here is being applied to determine the
handling qualities of a large flexible aircraft of Reference 2 in a longi-
tudinal tracking task with parametric variations in the undamped natural
frequencies of the two lowest frequency, symmetric elastic modes made to
induce varying amounts of mode interaction. The pilot rating is found by
using the technique of Reference 7.
Acknowledgement
A
The author wishes to thank Dr. Robert L, Swaim of Oklahoma State
University for his guidance and support. This work is supported by the
NASA Dryden Flight Research Center under Grant NSG 4018.
M
a
A	 4-
References
1, Chalk, C. R,, et al. "Background Information and User Guide for
MIL S-F-87858(ASG), Military Specification - Flying Qualities of
Piloted Airplanes." AFFDL-TR- 69 -72, Air Force Flight Dynamics
Laboratory, Bright-Patterson AFB, Ohio, 1969,
2. Swaim, R. L. and Yen, W. Y. "Effects of Dynamic Aeroelasticity on
Handling qualities and Pilot Ratings." AIAA paper 78-1365.
Proceedings of the ALmospheric Flight Mechanics Conference,
Palo Alto, CA, August 7-9, 1978.
3. Kleinman, D. L., Baron, S, and Levison, W. H, "A Control Theoretic
Approach to Manned-Vehicle Systems Analysis." IEEE Trans. Auto.
Contr., Vol. AC-16 (1971), 824-832.
4. Baron, S. and Berliner, J, "MANMOD 1975: Human Internal Models
and Science- Perception Models." Army Missile Research, Develop-
ment and Engineering, Redstone Arsenal, A1., 1975.
5. Chow, J. H., Allemong, J, J. and Kokoktovic, P. V, "Singular
Perturbation Analysis of Systems with Sustained High frequency
Oscillations." Automatics, Vol. 14 (1978), 271-279.
6. Haddad, A. H. "Linear Filtering of Singularly Perturbed Systems."
IEEE Trans. Auto, Contr., Vol, AC-21 (19*), 515-519.
7, Hess, R. A. "A Method for Generating Numerical Pilot Opinion
Ratings." NASA TM X 73101, 1976.
PAC
A
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Handling qualities of large flexible control-configured aircraft

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